Nuprl Lemma : continuous-abs-ext
∀[I:Interval]. ∀[f:I ⟶ℝ]. (f[x] continuous for x ∈ I ⇒ |f[x]| continuous for x ∈ I)
Proof
Definitions occuring in Statement :
continuous: f[x] continuous for x ∈ I,
rfun: I ⟶ℝ,
interval: Interval,
rabs: |x|,
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q
Definitions unfolded in proof :
continuous-minus,
continuous-max,
continuous-abs,
member: t ∈ T
Lemmas referenced :
continuous-abs,
continuous-minus,
continuous-max
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}[I:Interval]. \mforall{}[f:I {}\mrightarrow{}\mBbbR{}]. (f[x] continuous for x \mmember{} I {}\mRightarrow{} |f[x]| continuous for x \mmember{} I)
Date html generated:
2018_05_22-PM-02_17_47
Last ObjectModification:
2018_05_21-AM-00_32_49
Theory : reals
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